High School Solving Square Root & Quadratic Equations

[Einstein's Cat]

Let's say there's an equation

0 = √x - √x

I intend to make x the subject of the equation; however because it is a square root, there are numerous solutions; however can I just assume that

0= √x - -√x= 2√x

Can I now just rearrange this equation to make x the subject? In other words is the equation above equivalent to the equation below?

0= -√x -√x = -2√x

Would the same be true if there were roots in a quadratic equation?

 

[mfb]

Do you really expect that a-a=2a in general? Here a=sqrt(x).

What do you know about the solutions to the equation 0=a-a?

 

[DuckAmuck]

If something equals 0, you can flip the sign any way you want.
If x = 0, then -x = 0 as well

 

[Einstein's Cat]

Do you really expect that a-a=2a in general? Here a=sqrt(x).

What do you know about the solutions to the equation 0=a-a?

I think that as this applies to any number; the solutions is any number and therefore the equation is undefined.

 

[Mark44]

Let's say there's an equation

0 = √x - √x

Do you realize that the right side is equal to zero for any nonnegative real number x?

I intend to make x the subject of the equation; however because it is a square root, there are numerous solutions

Not sure what you mean by this. The symbol $\sqrt{x}$ has one value, assuming that $x \ge 0$.

; however can I just assume that

0= √x - -√x= 2√x

?
This is different from the equation you have at the top of your post.
The first equation you show is √x - √x = 0. The equation just above, when simplified is √x + √x = 0. These two equations are not equivalent.

Can I now just rearrange this equation to make x the subject? In other words is the equation above equivalent to the equation below?

0= -√x -√x = -2√x

Would the same be true if there were roots in a quadratic equation?

I don't understand what you're asking here.

 

[Einstein's Cat]

Do you realize that the right side is equal to zero for any nonnegative real number x?
Not sure what you mean by this. The symbol $\sqrt{x}$ has one value, assuming that $x \ge 0$.
?
This is different from the equation you have at the top of your post.
The first equation you show is √x - √x = 0. The equation just above, when simplified is √x + √x = 0. These two equations are not equivalent.

I don't understand what you're asking here.

I apologise for I am unable to express what I mean; this thread serves no purpose

 

[Mark44]

I apologise for I am unable to express what I mean; this thread serves no purpose

Thread closed.